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36.

Perpendicular are drawn  from points on the line   x+22=y+11=z3 to the  plane x+y+z=3 . The feet of perpendicular lie on the line


A) x5=y18=z213

B) x2=y13=z25

C) x4=y13=z27

D) x2=y17=z25



37.

For a>b>c>0, the distance between (1,1)  and the point of intersection of the lines ax+by+c=0  and bx+ay+c=0 is less than 

2\sqrt{2}  then 


A) a+b-c >0

B) a-b+c<0

C) a-b+c>0

D) a+b-c<0



38.

Let complex numbers \alpha  and \frac{1}{\alpha} lies on circles   (x-x_{0})^{2}+(y-y_{0})^{2}=r^{2}   and 

(x-x_{0})^{2}+(y-y_{0})^{2}=4r^{2} respectively.If z0=x0+iy0 satisfies the equation   2|z0|2=r2+2 , then |\alpha|  is equal to

 


A) \frac{1}{\sqrt{2}}

B) \frac{1}{2}

C) \frac{1}{\sqrt{7}}

D) \frac{1}{3}



39.

Let   PR=3\hat{i}+\hat{j}-2\hat{k}   and  SQ=\hat{i}-3\hat{j}-4\hat{k} determine diagonals of a parallelogram PQRS and

 PT=\hat{i}+2\hat{j}+3\hat{k}   be another vector . Then, the volume  of the parallelopiped determined by the vectors PT,PQ and PS is


A) 5

B) 20

C) 10

D) 30



40.

The value of cot \left\{\sum_{n=1}^{23}\cot^{-1}\left(1+\sum_{k=1}^{n}2k\right)\right\}  is 


A) \frac{23}{25}

B) \frac{25}{23}

C) \frac{23}{24}

D) \frac{24}{23}



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